They should have port talks on board and often show them on the tv. Check them out. You can also stop at their desk and ask where to go (they have maps and will list the shops that are safe to deal with-meaning youre purchases are guaranteed not to be fake). If youre looking for something in particular, ask as they will find out where to send you for it. They also sell a discount book filled with coupons. Were not big shoppers so we dont get one, but they do give you free perks (free totes in some stores, etc). Cayman has good shopping, Cozumel isnt bad (Im leary about some of those places selling jewelry-overpriced and the stuff doesnt look like its always good quality). My mom was into gemstones and has a beautiful collection of common and rare stones (which is now mine since shes gone). She was told by her gemologist not to buy from the shops as they mark them up and are not good quality. She has a tanzinite necklace that is so deep purple it looks like a sapphire. Its the highest quality you can buy. The ones you see in the stores are light purple-not good quality, but hey if you like it, go for it. A warning about opals: steer clear of the store ones as they are not cured long enough and will crack down the road.